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МатематикаГДЗ по алгебре 8 класс Макарычев ФГОС Задание 748
Задание 748
\[\boxed{\text{748.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
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\[\textbf{а)}\ (5x + 3)^{2} = 5 \cdot (x + 3)\] \[25x^{2} + 30x + 9 = 5x + 15\] \[25x^{2} + 25x - 6 = 0\] \[D = 625 + 600 = 1225\] \[x_{1,2} = \frac{- 25 \pm 35}{50} = \frac{1}{5};\ - \frac{6}{5}\] \[Ответ:при\ x = \left\{ - 1,2;0,2 \right\}.\] |
\[\textbf{б)}\ (3x + 10)^{2} = 3 \cdot (x + 10)\] \[9x^{2} + 60x + 100 = 3x + 30\] \[9x^{2} + 57x + 70 = 0\] \[D = 3249 - 2520 = 729 = 27^{2}\] \[x_{1,2} = \frac{- 57 \pm 27}{18} = - \frac{30}{18};\ - \frac{84}{18}\] \[x_{1} = - \frac{5}{3};\ \ x_{2} = - \frac{14}{3}\] \[Ответ:x = \left\{ - 1\frac{2}{3};\ - 4\frac{2}{3} \right\}.\] |
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\[\textbf{в)}\ (3x - 8)^{2} = 3x^{2} - 8x\] \[(3x - 8)^{2} - x \cdot (3x - 8) = 0\] \[(3x - 8)(3x - 8 - x) = 0\] \[3x - 8 = 0\ \ \ \ \ \ \ 2x - 8 = 0\] \[\ \ \ \ \ \ \ \ \ 3x = 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x = 8\] \[\ \ \ \ \ \ \ \ \ \ \ x = \frac{8}{3}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 4\] \[Ответ:x = \left\{ 2\frac{2}{3};4 \right\}.\] |
\[\textbf{г)}\ (4x + 5)^{2} = 5x^{2} + 4x\] \[16x^{2} + 40x + 25 = 5x^{2} + 4x\] \[11x^{2} + 36x + 25 = 0\] \[D = 1296 - 1100 = 196 = 14^{2}\] \[x_{1,2} = \frac{- 36 \pm 14}{22} = - 1;\ - \frac{25}{11}\] \[Ответ:x = \left\{ - 2\frac{3}{11}; - 1 \right\}.\] |
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\[\textbf{д)}\ (5x + 3)^{2} = 5x + 3\] \[(5x + 3)^{2} - (5x + 3) = 0\] \[(5x + 3)(5x + 3 - 1) = 0\] \[(5x + 3)(5x + 2) = 0\] \[5x + 3 = 0\ \ \ \ \ \ \ \ 5x + 2 = 0\] \[\ \ \ \ \ \ \ \ 5x = - 3\ \ \ \ \ \ \ \ \ \ \ \ \ 5x = - 2\] \[\ \ \ \ \ \ \ \ \ \ x = - \frac{3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{2}{5}\] \[Ответ:x = \left\{ - 0,4;\ - 0,6 \right\}.\] |
\[\textbf{е)}\ (5x + 3)^{2} = (3x + 5)^{2}\] \[25x^{2} + 30x + 9 = 9x^{2} + 30x + 25\] \[16x^{2} = 16\] \[x^{2} = 1\] \[x = \pm 1\] \[Ответ:x = \left\{ - 1;1 \right\}.\] |
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\[\textbf{ж)}\ (4x + 5)^{2} = 4 \cdot (x + 5)^{2}\] \[16x^{2} + 40x + 25 = 4x^{2} + 40x + 100\] \[12x^{2} = 75\] \[x^{2} = \frac{75}{12} = \frac{25}{4}\] \[x = \pm \frac{5}{2} = \pm 2,5\] \[Ответ:x = \left\{ - 2,5;2,5 \right\}.\] |
\[\textbf{з)}\ (2x + 10)^{2} = 4 \cdot (x + 5)^{2}\] \[4x^{2} + 40x + 100 = 4x^{2} + 40x + 100\] \[0 = 0\] \[Ответ:x - любое\ число.\ \] |
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